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Floor trading today serves primarily as the backdrop for financial television shows. The vast majority of securities trading is electronic, including that conducted by the NYSE itself. The electronic and futures businesses owned by parent company NYSE Euronext are far more valuable than its Manhattan trading floor. Atlanta-based IntercontinentalExchange Inc.ICE-0.44% has agreed to buy NYSE Euronext for $8.2 billion.

As recently as 2006, the NYSE's electronic and floor trading together represented 48% of U.S. stock trading volume. This year, it is half that at 24%, according to Tabb Group.

And yet, in other ways, the stock-exchanges business remains central to the smooth functioning of the new stock-trading landscape.

With high-frequency traders and privately operated systems called "dark pools" now representing half or more of all trading, mainstream investors rely more than ever on the continued openness of major public stock markets.

NYSE: A History

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Open trading in markets such as the NYSE ensures that investors can see the value, tick by tick, of the publicly traded companies that represent the vast majority of the nation's business activity. Many investors still turn to the Big Board as the official price-setter for the official opening and closing of stock prices.

Open trading on the New York Stock Exchange is still the best way to determine what price the market wants to pay for a stock, says Andrew Frankel, co-president of Stuart Frankel & Co., a brokerage firm. "We believe this is still a viable place to do business," says Mr. Frankel, whose firm trades on the floor and electronically.

The role that the exchange continues to play was in evidence following superstorm Sandy. When the storm hit, questions about the ability of the NYSE to get up and running were central to the decision to keep the U.S. stock market closed for two days.

So it isn't the historic real estate that matters in any sale of the NYSE. It is that any new owners face these two other challenges: ensuring that stock prices continue to be set in the open, and doing a better job of keeping the financial system running next time a crisis hits.

For people like Andy Walsh, it is too late to worry.

Mr. Walsh, 47 years old, got into the trading business in 1988, after a couple of years' study at the University of Richmond. A friend introduced him to a floor-trading firm at the old American Stock Exchange, now part of the NYSE. Business was so good that there seemed little reason to finish college.

By 1995, Mr. Walsh was working for a floor trader at the New York Stock Exchange called Olsen Securities Corp., and in 2003 he and a friend bought the business.

His best year was 2006. But within a few years, it became clear that floor trading was losing out to the speed and ease of electronic trading. Unable to sell his business, Mr. Walsh closed it at the end of 2010. Today, he drives a limousine part time and is looking for full-time work. He made about $360,000 in 2006, he says. "Last year, I made about $20,000."

His former partner works for a tree company doing a booming business pruning and removing trees after Sandy. Recently, Mr. Walsh was driving people to board a cruise liner when he ran into another old colleague from the trading floor. "He was down on the docks directing traffic for the cruise line," Mr. Walsh says.

Ted Weisberg still runs a trading firm called Seaport Securities Corp., which buys and sells shares on the floor of the NYSE.

Mr. Weisberg became a member of the exchange 43 years ago and has worked in the business for nearly 50 years. Ten years ago, Mr. Weisberg figures, the majority of his business was on the floor, but that is hardly the case today. Most of it is "upstairs," as the old hands put it, meaning at his offices near the exchange. Most is electronic.

Mr. Weisberg isn't a fan of high-frequency trading, computers and algorithms, all of which have prospered at the expense of openness, of mainstream clients and "at the expense of people both on and off the trading floor," he says.

He blames Congress and the Securities and Exchange Commission for being too quick to deregulate. "What has happened to the stock exchange and the trading floor in particular is very sad on a lot of levels, not just on a personal level," Mr. Weisberg says.

He isn't persuaded that the move toward low-margin, high-speed electronic trading was the best thing for long-term investors who are less interested in how many cents they pay for a trade than in an open, reliable system.

But he figures it is too late for him, at age 72, to do much about it.

Many in the securities business would argue with him, maintaining that electronic trading and computers have made the business cleaner, more efficient and less prone to abuse.

Whoever is right, the sale of the New York Stock Exchange to a new owner is more than a nostalgic event.

It is a wake-up call about the need to be sure that stock trading remains open and comprehensible to the institutions, individuals and public companies that rely on it—and to be sure that, in the next crisis, financial markets do a better job of staying open.

Corrections & Amplifications The Buttonwood Agreement that marked the birth of the New York Stock Exchange was signed in 1792. In an earlier version of this article, the date was incorrectly given as 1972 in a caption with a painting of the signing, which accompanied an article about the NYSE takeover agreement.

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